I like the pronunciation "Tescoss" as if it's an exotic Greek Island.
Logically speaking "Tesco's" would imply possession by a single person (ie. 'belonging to Tesco') since this is a faceless corporate, I would agree with you despite the fact that it ends up sounding like a country.
I suspect that what your Dad says is a leftover from a bygone era when shops were single outlets owned by one person or a family, so the possessive would make sense.
If I'm right EB, I would let the whole thing go and put it down to 'the olden days'. Go to the corner shop instead.



